Question

Assertion: 2²⁰ + 2²⁰ = 2²¹

Reason: a^m + aⁿ = a^{m + n}

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is true but R is false.

Explanation:

Analysis of Assertion and Reason

Assertion (A)

The assertion states that 2²⁰ + 2²⁰ = 2²¹.

This can be rewritten as 2 × 2²⁰. 

Using the property of exponents where a^m × aⁿ = a^m+n, this becomes 2¹ × 2²⁰ = 2¹⁺²⁰ = 2²¹.

Therefore, the assertion is true.

Reason (R)

The reason states that a^m + aⁿ = a^m+n.

This is a common misconception and is incorrect. The correct property for the product of powers with the same base is a^m × aⁿ = a^m+n. The reason provided incorrectly applies addition to the exponents when the bases are added, not multiplied.

Therefore, the reason is false.